I've removed Fusion Display from system tray because I open it rarely. However from time to time I require access to icon profiles (either save, or load). Is there a way to access these options without having to put the system tray icon back every time?

You can right-click any blank space on the DisplayFusion taskbar, or the TitleBar Buttons. You can also assign key combinations to the Desktop Icon Profiles on the DisplayFusion Settings > Functions tab.